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10 December, 06:47

Nathan walked on an asphalt pathway for 12 miles. He walked the 12 miles back to his car on a gravel road through the forest. On the asphalt he walked 2 miles per hour faster than on the gravel. The walk on the gravel took one hour longer than the walk on the asphalt. How fast did he walk on the gravel?

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Answers (2)
  1. 10 December, 07:01
    0
    Answer:4
  2. 10 December, 07:12
    0
    Answer: 4 miles/hour

    Step-by-step explanation:

    Distance walked on asphalt = Da = 12 miles

    Distance walked on gravel = Dg = 12miles

    time spent on asphalt = ta = ?

    time spent on gravel = tg = ?

    However, time spent on gravel was 1 hour longer than on asphalt

    Therefore,

    (tg) hrs - (ta) hrs = 1 hr

    tg = ta + 1 ... Equation 1

    Magnitude of velocity or speed

    Vg = speed on gravel

    Va = speed on asphalt

    However, he walked 2 miles per hour faster on asphalt than on gravel

    Therefore,

    Va = Vg + 2 ... Equation 2

    Note that all velocity values will carry the miles/hr unit

    However,

    Velocity = distance/time

    Da/ta = (Dg/tg + 2) miles/hour

    12/ta = [ (12/tg) + 2] ... Equation 3

    But tg = ta + 1 (from equation 1)

    We substitute for tg in equation 3

    12/ta = [ (12/ta+1) + 2] ... Equation 4

    Taking the LCM of the the fraction, we have

    12/ta = [12+2 (ta+1) ]/ta+1

    Opening the inner bracket, we have

    12/ta = (12+2ta+2) / ta+1

    Cross multiplying, we have

    12ta+2ta2+2ta = 12ta+12

    We can eliminate 12ta as it appears on both sides

    2ta2 + 2ta - 12 = 0

    This has become q quadratic equation, we factorize into;

    (2ta - 4) (ta+3) = 0

    2ta - 4 = 0

    2ta = 4

    ta = 4/2

    ta = 2

    Since tg = ta + 1

    tg = 2+1

    = 3hours

    Vg = 12/tg

    = 12/3 = 4 miles/hour

    His speed on the gravel was 4miles/hour
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